Topological free volume and quasi-glassy dynamics in melt of ring polymers

Abstract

Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first construct a phenomenological free energy which enables one to qnaitify the degree of topological crowding measured by the coordination number. Then we pinpoint a key role of the cooperative dynamics of neighboring rings, which is responsible for an anomalous dependence of the global structural relaxation (diffusion) time on ring length. Predictions on molecular weight dependence of both static (ring size, coordination number) and dynamic (relaxation time, diffusion coefficient) quantities are in very good agreement with reported numerical simulations. Throughout the discussion, the entanglement length $N_e$ is assumed to be a unique characteristic length for the topological constraint, hence, all the physical quantities are universally described in terms of the rescaled chain length $N/N_e$. Finally, we discuss how the dense solution of rings is analogous yet different from ordinary glassy systems.

10 pages, 5 figures

References in corpus (7)

• Theoretical perspective on the glass transition and amorphous materials
• Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: I. Statics
• Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: II. Dynamics
• Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers
• Slowing down of ring polymer diffusion caused by inter-ring threading
• Effect of Topology on the Conformations of Ring Polymers
• Miscibility Phase Diagram of Ring Polymer Blends: A Topological Effect

Cited by in corpus (5)

• Persistence Homology Of Entangled Rings
• Effects of chain length on Rouse modes and non-Gaussianity in linear and ring polymer melts
• Unraveling the glass-like dynamic heterogeneity in ring polymer melts: From semi-flexible to stiff chain
• Phase separation in soft repulsive polymer mixtures: foundation and implication for chromatin organization
• Quantifying the mobility of chromatin during embryogenesis: Nuclear size matters